Development and investigation of the effectiveness of the particle swarm optimization algorithm

Investigation of effectiveness of Particle Swarm Optimization algorithm was conducted by solving test constrained and unconstrained multi-criterion problems. The maximum number of particles, which could be stored in the archive of non-dominated solutions, was set up for algorithm’s work. Number of particles in the archive was different for all problems. For solving constrained optimization problems was used method of the dynamic penalties. When finding solutions for problems archive filled partially. Researches showed that increasing of number of criterions leads increasing of algorithms’ effectiveness. So, for example, archive of the non-dominated solutions was filled on the average on 20–30 % when constrained problems were solved by using standard PSO and also by using binary PSO. Advantage of the standard PSO was only in time that was spent for one program run. And again algorithms’ results didn’t differ significantly. Number of particles and generations was about the same as it was when unconstrained problems were solved. Solving one constrained problem, feature of which was that, there was no point from Pareto set in the feasible region, required notable increase in population size. And in the end points, that was obtained, were on the part of the boundary of feasible region, which was the closest to the Pareto set. Results that were obtained by using both standard and binary PSO were almost the same.

After all the investigations conducted, two real-world problems were solved: problem of formation of optimal investment portfolio of the enterprise and problem of formation of optimal loan portfolio of the bank. Besides, first problem was solved as in one-criterion definition so in the multi-criterion definition.

Ш. А. Ахмедова

РАЗРАБОТКА И ИССЛЕДОВАНИЕ ЭФФЕКТИВНОСТИ СТАЙНОГО АЛГОРИТМА ОПТИМИЗАЦИИ

Проведены исследования эффективности стайного алгоритма оптимизации (PSO) с вещественными и бинарными частицами при решении задач условной и безусловной одно- и многокритериальной оптимизации. Разработаны также параллельные модификации обоих алгоритмов и решены две реальные практические задачи.